This article presents an overview of hands-on teaching methodology seen as a form of concurrent teaching, as opposed to traditional sequential teaching. The reasons for its implementation are discussed, together with its use in a range of different disciplines and the difficulties to be expected in traditional universities. The case of PUC-Rio is analyzed as an example.

The core idea behind hands-on teaching is not new: to expose students to concrete problems so that they are required to project and construct a solution in conditions as close as possible to its future use, seeking the relevant information as it becomes necessary. The point is to go beyond the classical interpretation of "learning by doing" -- a form of training based on example and repetition, in which the student follows more or less prefixed protocols -- and to lead the student to a representation of the problem placed in its context. In this way, the student will go in search of the necessary knowledge and project the possible solutions, choosing the one that is most appropriate for present conditions, applying it and verifying it (or managing it), while reflecting on the tools used and the general process of problem-solving. The object is to give students formative training that will allow them to identify and solve new problems, to create in a rational way their own solution protocols, rather than merely repeat known solutions to well-established problems. On a deeper level, the object is to develop the student's reflective abstraction (in Piaget's sense of the term) in relation to engineering, together with an enterprising attitude when facing challenges.

The next section is a critique of traditional sequential college teaching, focusing on a set of contradictions between its results and the actual formative needs of engineers today. The section after that discusses the characteristics that college training must develop in response to the critique presented earlier, and describes hands-on methodology -- conceived as a form of concurrent teaching -- proposing it as a solution to the contradictions discussed before. The last two sections examine the difficulties in the implementation of this methodology, considering different areas of knowledge and the experiments tried out in PUC-Rio.

SEQUENTIAL TEACHING: DEFINITION AND CONTRADICTIONS

A common characteristic of most engineering courses is sequential and compartmentalized teaching: the curriculum is based on the logical structure of knowledge. First come the basic theories, then the advanced theories and demonstrative laboratory work (which does no more than exemplify the theories), and finally the applications. The typical engineering major gets a chance to solve concrete problems (if at all) only in his or her end-of-course paper, when his or her training is completed. Such a curriculum is wholly specified on the basis of fixed contents, no consideration being given to the attitudes to be developed in students. Knowledge is subdivided into specific courses, rigidly tied together by lists of prerequisites but unconnected as far as assignments and evaluations are concerned: there are no multidisciplinary assignments. Naturally, teaching sequences become fixed and compulsory, except for a body of additional information seen as of secondary importance.

This process, which organizes curricula from the vantage point of one who has already mastered the entire content, points to a conception of knowledge as a large, fixed body of rigid and unchangeable certainties, with an addendum of subordinate information, as mentioned above. It tends to present problems of engineering confusing them with solution techniques, in the form of rigid protocols deduced from earlier theory. Taken to its ultimate consequences, the teaching methodology built into this process makes students passive, privileging "absorbent" students, to use Kolb's term, at the expense of students with other learning styles (accommodating, divergent, and convergent).

Now, neither the historical process of the knowledge-building⁽¹⁾ nor the psychological construction of the capacity for abstraction and of abstract concepts themselves⁽²⁾ follow the sequential process defined on the basis of the logical organization of final contents. The very structure of knowledge, as it is conceived by epistemologists today,⁽³⁾ is dynamic; all that can be had is "partial certainty"; theories are always awaiting possible refutation; knowledge evolves in opposition to earlier knowledge. Enunciation of a concept pure and simple can integrate its name into the student's discourse, but not into the student's universe of meanings. The construction of a concept by a student (or by science) advances in blocks and works against early conceptions, which must be discovered, assimilated by consciousness, and questioned; demonstration is not enough.⁽⁴⁾ Traditional teaching, even when it includes plenty of classroom assignments, does no more than train the student in the use of the teacher's discourse, and fails to cause any major change in the student's preconceptions.

The situation is just as critical in the teaching of the state of technique. The turnover of techniques and even of technological principles now takes place at such breakneck pace that the techniques learned by a student around the middle of his or her engineering course are obsolete by the time the student graduates. It has been estimated that fifty percent of the techniques taught in engineering courses will no longer be cited or used after five years.⁽⁵⁾ The new division of labor, a consequence of standardization and automation, restructures problems and technologies faster than engineering curricula can change.

Two well-known paradoxes arise in consequence of sequential teaching. The first is the multidisciplinarity paradox, a result of the rigid compartmentalization of knowledge: increasingly, concrete problems require training in different disciplines and can be tackled only on the graduate-school level. The training provided by any one discipline seems incomplete when confronted with the real world. The second is the paradox of the specialist, a consequence of the concept of knowledge underlying sequential teaching: it is impossible to train an engineer in all the knowledge that he or she may come to be expected to have, even if one is dealing with a genius, due to limitations of extension (a huge content that must be approached from an in-depth perspective) and time (the knowledge will have long become obsolete by the time it is mastered).

Experiments with the purpose of facing these two paradoxes locally have been successful only in courses with secondary status (having no fixed content or not counting as prerequisites) or in extracurricular form (projects in introduction-to-science programs). Examples of this are laboratory sessions in which a concept is built up by means of experiments, which always clash with the curricular program and with the teaching of theory. So are experimental courses that are forgotten as soon as the teachers responsible for them stop teaching them because they cannot be integrated into the structure of the official curriculum (instances of these will be given in the next-to-last section).

In the following section it will be shown that these two paradoxes disappear when the concepts of knowledge and training are changed -- that is, once a new teaching paradigm is adopted.

A NEW PARADIGM: CONCURRENT TEACHING

The analysis above shows that the function of teaching in present-day society cannot be simply that of conveying contents, but must consist basically in stimulating the ability to learn and the development of a problem-solving attitude. Engineers must know how to update themselves: they must be able to manage their own information flow, know how to represent problems and to look for the knowledge and techniques necessary for solving them at the moment where they are actually needed. The construction of knowledge must be an ongoing process, so that engineers must be trained in the ability to develop it. The content of the engineering course should be seen as no more than the present state of knowledge, providing a language and a number of concepts with which to formulate problems and examples that are temporarily useful.

In the present-day world, an engineer must be able to utilize technological innovations, engage in team work, express his or her ideas, argue (an ability that provides an in-depth measure of his or her reflective ability), create, develop, and manage projects. In terms of psychological traits, engineers must be enterprising -- that is, capable of building their own future, identifying problems, carving out a niche for themselves, and actualizing their ambitions. To return to the pedagogic context, what is required is the active student's intelligence, rather than the passive student's memory.

Concurrent teaching is a pedagogic paradigm that attempts to meet these requirements. Students are exposed, in groups, to problems as close as possible to concrete reality, and they have to search for relevant contents as dictated by actual need. They must resort to laboratories and libraries, which are seen as environments and tools to be used by students as their inventiveness and ability to experiment dictates. Contents are integrated by the inner logic of the problem being tackled, to the extent that they contribute to its solution. Students do not try to learn all the techniques applicable to every problem that could ever arise in their area. Instead, they aim to acquire a coherent overview of these techniques and ways that will allow them to communicate with clients, teachers and classmates and to choose their own ways. They probe more deeply only into the aspect of the problem that is relevant to them.⁽⁶⁾ This encourages structured and continuous learning, so that the student is led to program his or her own learning process. Also encouraged is technical intervention in concrete problems, which is conducive to an enterprising attitude. Students must see themselves as engineers from the beginning.

Some advantages are evident. Knowledge is presented integrated into the student's reality and constructed within his or her own universe of meaning. Multidisciplinarity comes naturally. Team work and the existence of "clients" require formal representation of knowledge and the use of reflective abstraction, not mere mimicry of the teacher's discourse. Evaluation can be made objective by resorting to the opinion of the external "clients," requiring not a certain amount of content but instead effectiveness in the solution of problems that require the desired attitude. Students must constantly face intellectual challenges posed by concrete problems associated with their goals. This, it is to be hoped, will promote increased motivation and make learning an enjoyable process.

Clearly, this implies a drastic change in the teacher's attitude: the teacher is no longer the proprietor of knowledge, but a facilitator and a questioner. He or she must not present ready-made protocols, but instead do no more than suggest and point out possible paths. Occasionally the teacher should challenge students' beliefs, by means of a didactics of counterexamples,⁽⁷⁾ in order to stimulate critical thinking and encourage explanations and changes in beliefs. The teacher should select problems that are open enough to touch on all points of interest, fixing a context so that students will not become too unfocused. He or she should set out the tools and the difficulties, providing students with orientation without making decisions for them, questioning instead of answering. Students must be given the freedom to make their own mistakes -- and correct their mistakes as well. The teacher must be prepared to avoid the pitfalls implied by this kind of methodology -- to be examined in the next section -- and to evaluate students and project directly on the basis of the course's objectives. This last requirement is essential, for students tend to see evaluation as the key concept around which their activities are centered.

The choice of problems and their contexts is essential for the success of such a methodology. This choice will depend on the type of underlying content and on the objectives of the course. This will be discussed in later sections. Below is a table of antinomies between traditional teaching and the paradigm proposed here. These antinomies can be brought out by contrasting the pure types of sequential and concurrent teaching. As the examples will make clear, these pure types do not exist in actual practice, but they are helpful as theoretical resources.

Two ways naturally lead to the teaching paradigm proposed here. One is the genetic epistemology of Piaget and his collaborators,⁽⁸⁾ which shows that intelligence (in its various stages, including that of reflective abstraction) and knowledge (including scientific knowledge) are generated by active processes these authors refer to as balancing by self-regulation. This requires action, trial and error, correction, the facing of challenges and problem solving -- known in the literature as "projects elaborated by students" -- until concepts are constructed in their networks of relations. Project-based teaching has been a major topic in pedagogic research on elementary and secondary education in recent years, see the section on examples.

Another way is to attempt to project teaching methodology as a means to a given end: to train engineers able to meet the demands that the twenty-first century will probably make. A careful examination of goals to be reached (the "new" engineer), of existing pedagogic methodologies, and of students' actual conditions (a pragmatic view of their motivations and abilities) naturally leads to the paradigm described above. In it, students are made to experience the activities of engineering, developing the abilities required by the problems posed.⁽⁹⁾ These two ways are complementary: the first lays down the psychological bases for the second, while the second points to the urgent need for a new sort of training.

COMMENTS ON THE IMPLEMENTATION OF THE NEW PARADIGM

The first point made in all experiments we know of concerns the difficulty of following a classical curriculum, particularly when the contents of such a curriculum have been designed to fill an entire school term adopting sequential methodology. When motivating projects are employed, covering the curriculum takes much more time than when sequential presentation is adopted. It is the paradox of the specialist once again: what is required is a change in the underlying conception of knowledge, which is contradictory with the objective of achieving full coverage of this content. The solution that has been adopted is to give up classical contents, redefining objectives in terms of classes of problems to be examined.

This new approach reformulates the problem in a somewhat different way: the student must understand the terms of the problem in order to recognize it and attempt to solve it. The solution is to choose a sequence of problems requiring that students will develop the concepts and the language all the way to the level required. The crucial point, and the one that is most laborious in the new pedagogic strategy, is how to choose a sequence of problems in terms of difficulty and of necessary means without predetermining students' activities.

It is not possible to retrace the historical construction of the concepts, reconstructing each theory one by one. Not only are students already placed in a different episteme and a different universe of meanings (and the understanding of the history of science requires a huge hermeneutic effort), but also the time necessary for this would be too long. The sequence of problems adopted should be based on students' preconceptions and their earlier knowledge, taking into account the availability of problem-solving material and access to necessary knowledge.

Often the problems that are of interest do not fit into previously defined courses, for they are naturally interdisciplinary. This partly explains the growing interest in projects of introduction to science (financed by government agencies), which are so useful to students but are necessarily extracurricular (when the curricula in question are sequential, that is). This problem is even more serious when the project calls for laboratory experiments or off-campus field work: reality resists and deadlines are not observed -- at least if we are interested in having thoroughly developed projects with high pedagogic value. The new pedagogic proposal clashes with the conventional formal structure of engineering courses -- which requires that courses begin and end at well-defined times -- and demands "transdisciplinary" projects and teams.

Nonetheless, there are subjects that perhaps must be approached from a traditional angle, using lectures and apprenticeship. How to teach mathematics students to demonstrate theorems without asking them to present such demonstrations or giving them illuminating examples? How to understand the exhaustive nature of physical theories without an overview presented by a lecturer? The solution is perhaps to be found in an intelligent combination of problems that motivate theories and sets of conferences on the relevant theories. Here scientific curiosity (which must be aroused) is the most important driving force.

In another departure from formal-structure pedagogy, the new approach forgoes completeness as a goal in the training of engineering students in favor of furthering the development of the enterprising spirit. This implies changes in evaluation, which no longer applies to the means (mastery of the teacher's discourse, ability to perform certain calculations or recognize certain formulas), but instead to the goals of the course (changes in behavior, development of intelligence and aptitudes, problem-solving ability). This type of evaluation is much more difficult to achieve than the conventional kind. In addition, it is necessary to face the thorny issue of evaluating team work, taking into consideration both the ability to work with others and individual performance. The methods of cooperative teaching are useful here.⁽¹⁰⁾

Here are a few summary comments on hands-on methodology:

For the teacher, it implies additional work, at least during the stage of preparation of the course, since the teacher must follow the students' rationale rather than his or her own. More explicitly:

• The teacher must find concrete problems that are on a level accessible to students and that require the use of relevant concepts and techniques.
• The teacher must predict, in the classroom sequence, the various probable paths in the interactions between student and teacher, machine and student, student and student, as well as mistakes and revisions: classroom dynamics becomes much more complex.
• The teacher must consider the asynchronism of students in problem-solving so as to make it possible for an interchange of experiences to take place: When should the session be interrupted in order to present a general explanation? When should the teacher suggest that a student ask a classmate for an explanation? When should the groups be brought together for intermediary discussions? How should the projects' timetable be controlled? How to encourage interaction between the various groups?
• The teacher must prepare carefully a minimal theoretical background, so that the terminology will be understood and the problems will be identified, but at the same time theoretical lectures should be avoided as much as possible.

Students cannot make progress unless concepts are truly grasped. This means that projects should not be solved by means of ready-made solutions and algorithms.

Beware of those students who just want to understand the particular problem in question and learn the particular algorithm used. The typical question asked by these students is: How do you solve it? If too many explanations are offered, the student may take in the algorithms and the discourse on the concepts but fail to learn the methodologies and concepts themselves. In other words, the student reproduces the teacher's discourse without actually understanding the problem.

The teacher should provide answers while simultaneously time questioning, opening new avenues and challenging preconceptions; give suggestions rather than display omniscience; point the way rather than hand out solutions.

There must be easy access to sources of information (libraries, the Internet, databases, patent banks, etc.). Reliance on textbooks as facilitating summaries should be avoided; students should instead be encouraged to consult a variety of sources.

EXAMPLES OF HANDS-ON ACTIVITIES

Here are some examples of existing teaching activities that follow the hands-on paradigm, to be discussed in the last section:⁽¹¹⁾

Technological challenges: the international contest for the construction of a mini-dune buggy, and the contest for the construction of an environment-friendly refrigerated drinking fountain (the latter project is a part of PUC-Rio's Program REENGE-2).

Projects in introduction to science and technology, at present as extracurricular activities, although financed by government agencies.

End-of-course papers, when they include a complete project.

Project courses, the main object of which is to study an engineering problem, so that the student is forced to work as a problem solver. For instance, Introduction to Engineering II, with a project for the use of solar energy for powering the walkie-talkies of the PUC-Rio security guards, presented during the second term of 1996.

Courses developed on the basis of a specific project: the problem presented gives rise to situations that require the study of the content of the course. An example is the engineering course at Besançon, France, in which the study of a washing machine provides the backbone for the first year of the course.

Courses in which the evaluation centers on a project that requires direct experience of the subject in question. An example is the Product Project course at PUC-Rio's Department of Industrial Engineering: in order to pass the course, a student must present a patent granted to him or her by Brazil's National Institute of Industrial Property (INPI). That is, students are required to produce an invention and get a patent for it. This course was very popular and pedagogically successful as long as it imposed this requirement.

Courses using a set of partial projects. These courses rely partly on lectures, partly on assigned projects that provide the basis for student evaluation. For instance, the course on Controls and Servomechanisms (when taught by one of the authors of the present paper), at PUC-Rio's Department of Electrical Engineering.

Courses based on specific challenges or requiring inventive constructions. Examples are Prof. Geovan Tavares's Calculus II course, using 3D-Vis software, and Prof. Ruy Milidiu's Introduction to Computer Science course, using a multimedia lab, both at PUC-Rio.

Comparable examples in secondary education are Project Amora at Colégio de Aplicação da UFRGS⁽¹²⁾ and the Escola do Futuro at USP. These are recent Brazilian experiments that are already yielding positive results.

CONCLUSIONS

The examples above underscore the difficulties implied by implementation of the new paradigm in an engineering course. Some of these experiments are extracurricular, and they can be integrated into regular curricula only if the latter are no longer organized by terms. Other experiments require that the division of the subject matter into courses be changed, on the basis of sequences of problems of increasing complexity rather than of content, as is done at present. Finally, there are contents that could not be handled in the new format, so that a concurrent-teaching curriculum might have to include islands of sequential teaching.

The equipment must be adapted. It is necessary to have laboratories providing support for the development of projects guided by students' imagination. Also, easier access to libraries, the Internet, specialists, and companies is needed.

The distribution of time must change, for with the new methodology much of the work takes place outside the classroom, in the laboratory or the field. It is no longer possible to take up students' entire time with detailed theoretical lectures and repetitive exercises. The classroom must change, and concepts of distance learning will have to be adopted.

But the most important change is in the teacher-student relationship. The major obstacle is in the training of teachers; it is here that creative, responsible, and enterprising people are needed.

REFERENCES

^i.See T. Kuhn, The Origin of Scientific Revolutions.

^ii. See Piaget and others, The Children's Psychology and Genetic Episthemology.

^iii. See the works of Bachelard, Popper and Piaget.

^iv. See Bachelard, La Formation du Sprit Scientifique.

^v. See Drucker, Harward Bus. Review, May, 1990, pp. 29-40.

^vi. This implies a radical change in the representation of the knowledge to be acquired.

^vii. See Bachelard, op. cit.

^viii. See Piaget, op. cit.

^ix. See Longo, Introduction of the REENGE International Seminar, Rio de Janeiro, 1995 and da Silveira at. all., Notas Sobre o Curso de Engenharia, Nota Interna CTC/PUC-Rio, 1995.

^x. See Paskusz, Comunity Building Through Cooperative Learning, 1994ASEE An. Conf. Proc., pp. 1423 - 1426.

^xi. For more extensive reports on some of these experiments, see hhttp://www.dctc.puc-rio.br, where they are described as activities of Project REENGE/PUC-Rio.

^xii.See http://www.psico.ufrgs.br

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